Question

a. At this instant, is the particle in FIGURE Q4.1 speeding up, slowing down, or traveling at constant speed?

b. Is this particle curving to the right, curving to the left, or traveling straight?

Short answer

a. It slow down the particle.

b. The particle is curving to the left.

Step-by-step solution

Part.a.

Acceleration: rate of change of velocity with respect to time is known as acceleration. The formula to find the instantaneous acceleration is as follows,

$\overrightarrow{a}=\frac{d\overrightarrow{v}}{dt}$

Here $\overrightarrow{a}$is the instantaneous acceleration, $d\overrightarrow{v}$is small change in velocity and dt is the small change in time.

Consider the following diagram.

The acceleration $\overrightarrow{a}$is divided into two components, Perpendicular component $\left(a_{\perp }\right)$and parallel component$\left(a_{\Vert }\right)$to the velocity. The parallel component of the acceleration $\left(a_{\Vert }\right)$is opposite direction to the velocity vector$\left(\overrightarrow{v}\right)$therefore it slow down the particle.

Part.b.

The direction of perpendicular component $\left(a_{\perp }\right)$of the acceleration vector $\overrightarrow{a}$is to the left. It will change the direction of the particle to the left. Therefore, the particle is curving to the left.